Question

The National Bank of Germany is opening a new bank teller. Management estimates that customers will arrive at the rate of 10 per hour. The teller who will staff the window can serve customers at the rate of one every four minutes.

Assuming Poisson arrivals and exponential service, find:

Average number of customers in the system.

Average time in the system.

Average waiting time in the line.

Average number of customers in the line.

Utilization of the teller.

Answer 1

Given, Arrival rate , = 10 Now Service rate = = 60/4= 15

Now , Using the various formula of the  Poisson arrivals and exponential service, We can easily calculate the following,

1) utilization of the teller , = / = 10/15= 0.67 or 67 %

2) Avergae number of customers in the line = Square of / ( - )

= 100/15 5= 20/15= 1.33 customers

3) Avergae number of customer in the system = / -

= 10/ 15-10= 10/5= 2 customers

4) Average waiting time in the line is = Avergae no. of customers in the line / Arrival rate ( )

= 1.33/10= 0.13 hours or 7.8 minutes

5) Average waiting time in the system = Avg. no. of customers in the system / Arrival rate ( )

= 2/ 10 = 0.20 or 12 minutes